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Non-additivity of the fixed point property for tree-like continua

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Hagopian C., Marsh M.

Fundamenta Mathematicae

2015

tom 231

nr 2

113-137

We investigate the fixed point property for tree-like continua that are unions of tree-like continua. We obtain a positive result if finitely many tree-like continua with the fixed point property have dendrites for pairwise intersections. Using Bellamy's seminal example, we define (i) a countable wedge X̂ of tree-like continua, each having the fpp, and X̂ admitting a fixed-point-free homeomorphism, and (ii) two tree-like continua H and K such that H, K, and H∩ K have the fixed point property, but H ∪ K admits a fixed-point-free homeomorphism. In an appendix we verify some of the properties of Bellamy's continuum.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Hagopian C.

1 Marsh M.

1 2015

Wyniki wyszukiwania

Non-additivity of the fixed point property for tree-like continua